The Panorama of Spin Matrix Theory

Abstract

Spin Matrix theory describes near-BPS limits of $\mathcal{N}=4$ SYM theory, which enables us to probe finite $N$ effects like D-branes and black hole physics. In previous works, we have developed the spherical reduction and spin chain methods to construct Spin Matrix theory for various limits. In this paper, by considering a supercharge $\mathcal{Q}$ which is cubic in terms of the letters, we construct the Hamiltonian of the largest Spin Matrix theory of $\mathcal{N}=4$ SYM, called the PSU$(1,2|3)$ Spin Matrix theory, as $H=\{\mathcal{Q},{\mathcal{Q}}^{†}\}$. We show the resulting Hamiltonian is automatically positive definite and manifestly invariant under supersymmetry. The Hamiltonian is made of basic blocks which transform as supermultiplets. A novel feature of this Hamiltonian is its division into D-terms and F-terms that are separately invariant under PSU$(1,2|3)$ symmetry and positive definite. As all the other Spin Matrix theories arising from $\mathcal{N}=4$ SYM can be acquired by turning off certain letters in the theory, we consider our work as revealing the "Panorama" of Spin Matrix theory.

arXiv comment32+11 pages, 3 figures; v2: minor changes; v3: journal version with minor changes

References in corpus (74)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Review of AdS/CFT Integrability: An Overview
• An Index for 4 dimensional Super Conformal Theories
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Infinite Chiral Symmetry in Four Dimensions
• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• The su(2|3) Dynamic Spin Chain
• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Supersymmetric multi-charge AdS_5 black holes
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• Fivebranes from gauge theory
• Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• Nonrelativistic String Theory and T-Duality
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• BMN Gauge Theory as a Quantum Mechanical System
• String Theory and String Newton-Cartan Geometry
• Nonplanar Integrability
• Relating non-relativistic string theories
• Comments on 1/16 BPS Quantum States and Classical Configurations
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Aspects of Nonrelativistic Strings
• Nonrelativistic String Theory in Background Fields
• Three-dimensional dualities with bosons and fermions
• Torsional string Newton-Cartan geometry for non-relativistic strings
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Words to describe a black hole
• 1/16 BPS States in N=4 SYM
• Quantum Mechanical Sectors in Thermal N=4 Super Yang-Mills on RxS^3
• Residues, modularity, and the Cardy limit of the 4d $\mathcal{N}=4$ superconformal index
• Torsional Newton Cartan gravity from non-relativistic strings
• A worldsheet supersymmetric Newton-Cartan string
• On the Non-Relativistic Expansion of Closed Bosonic Strings
• Matching the Hagedorn temperature in AdS/CFT
• An Action for Extended String Newton-Cartan Gravity
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Torsional Deformation of Nonrelativistic String Theory
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• T-Duality in Nonrelativistic Open String Theory
• AdS${}_5$ Black Hole Entropy near the BPS Limit
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Nonrelativistic Approximations of Closed Bosonic String Theory
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Quasilocality of joining/splitting strings from coherent states
• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Nonplanar Integrability: Beyond the SU(2) Sector
• Superstring sigma models from spin chains: the SU(1,1|1) case
• Interacting Giant Gravitons from Spin Matrix Theory
• BPS coherent states and localization
• Magnetic Heisenberg-chain/pp-wave correspondence
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Sigma model from SU(1,1|2) spin chain
• The su(2|3) Undynamic Spin Chain
• Nonrelativistic Corners of $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory
• Renormalization properties of a Galilean Wess-Zumino model
• Semiclassical dynamics for torsional Newton-Cartan strings
• Modularity of supersymmetric partition functions
• Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Supersymmetric Galilean Electrodynamics
• Multispin magnons from Spin-Matrix strings on $Ad{S}_5\times S^5$
• On Non-Relativistic Supersymmetry and its Spontaneous Breaking
• Chiral 2D "Strange Metals" from N = 4 SYM
• Boson-fermion duality in four dimensions

Cited by in corpus (7)

• Aspects of Non-Relativistic Quantum Field Theories
• Worldsheet Formalism for Decoupling Limits in String Theory
• Matrix Theory Reloaded: A BPS Road to Holography
• Longitudinal Galilean and Carrollian limits of non-relativistic strings
• Interior analysis, stretched technique and bubbling geometries
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory